After weeks of maneuvering behind the scenes, AB InBev has made its play for SABMiller Plc with a bid valuing the company at $104.1 billion and setting up the world’s biggest merger battle this year.

The world’s largest brewing group went public with an improved offer Wednesday after SABMiller’s unanimously rejected two earlier ones (“without meaningful engagement,” AB InBev said sourly in its statement).

SABMiller immediately issued its own statement saying it still didn’t like the terms of the new offer, which would give its public shareholders 42.15 pounds a share in cash, a premium of 44% over where the shares were trading before news of AB InBev’s intention to bid leaked out last month. Update: SABMiller rejected AB InBev’s latest offer, CNBC reports.

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SABMiller’s strategic shareholders, who hold 41% of the company’s stock, would receive a lower offer worth 37.49 a share paid overwhelmingly in the form of a new class of unlisted share with a five-year lock-up period (a premium of only 28%). In what might prove to be a crucial split in the board, SABMiller’s biggest shareholder Altria Inc. has said it would accept that offer.

The share component of the deal partially addresses on the main concerns over it–namely, that AB InBev would be forced to take on too much debt to finance it. The new shares would pay the same pro rata dividends and voting rights as AB InBev’s listed stock.

SABMiller’s chairman Jan du Plessis said in a company statement that the new offer still undervalues the company “very substantially.” However, the argument appeared to be undermined by the fact tobacco group Altria Inc. , which is the group’s largest shareholder with around 27%, said that the lower, share-based offer was plenty good enough.”

Altria said in a statement that “a combination of these two companies would create significant value for all SABMiller shareholders,” and that “Altria supports a proposal of 42.15 pounds…and, subject to finalization of terms, would be prepared to elect the partial share alternative.” It urged the board to “engage promptly and constructively with AB InBev to agree on the terms of a recommended offer.”

However, SABMiller’s other major shareholder, the Colombian Santo Domingo family, doesn’t appear to like the deal as much. According to theFinancial Times, InBev said in a later statement that “it does not currently have the support” of BevCo Ltd., the family’s holding.

By contrast, AB InBev stressed that the global footprint of the combined group would be “largely complementary”, with SABMiller’s strength in Africa and Latin America the key element in completing the group’s global presence.